Calculus 45S

A window through the walls of our classroom. This is an interactive learning ecology for students and parents in my Calculus 45S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Thanks to all our listeners. We might get one more published during this school year but this may be the last until September. In any case feel free to let us know your thoughts about what you heard; every comment is appreciated.

In this episode of Student Voices Justice, Lawrence, and Richard talk about how they put together their Developing Expert Voices project and what they learned in the process: how they they best learn math, how it can best be taught, and many other incidental things like team work and organizational skills.

They have titled their project with one of my favourite reminders to all my students: Mathematics is the Science of Patterns. If you watch any of the video content they created you'll hear several "in jokes", listen for them. Without any further ado, here is the podcast. A copy of the poster they made for their work is below.

Monday, May 26, 2008

At the beginning of the class, we were asked to find the derivatives of the above functions. Needless to say, we found it difficult... NOT. It's 2x for all functions. And then we were given the derivative, f ' (x) = x and were asked to find the parent function. We were quite stumped at first, but then managed to figure it out. We had to go back to a previous lesson since we were asked whether if given a constant and a function and if we had to find the derivative of the function, does the constant play a role? No, it doesn't. Anyway, we were asked to find the parent function of the derivative f ' (x) = x. If x is the derivative, then obviously the parent function is x2. But the derivative of x2 is 2x and the derivative we want is x. So we figured, we have to multiply 2x by 1/2 to get x. From that, we got the parent function, which is 1/2x2. Mr. K then asked us, what about if I give you the derivative x2? What would be its parent function? We then thought about it. If x2 is the derivative, obviously the parent function is x3. But the derivative of that function will give us 3x2, which we don't want since we're given the derivative x2. So we thought multiplying 3x2 by 1/3 would give us x2. We reckon that the parent function is 1/3x3. From that we came up with a rule for all power functions, which is:

We then made anti-derivative rules for almost all derivative rules we remember. Mr. K said that the anti-derivative rules for the product and quotient rule are much more complicated and we won't be taking it until First Year University Calculus, so yeah.

Now this is where I explain the C part in the rule:

f ' (x) = xn -------> f (x) = xn+1/n+1 + C, where C is the constant

We can't really findC not unless we're given a point in the graph.C is basically the y-intercept, but if we're just given the derivative and asked to solve for the parent function, all we can do is find the parent function and then + C, not unless we're given a point in the graph.Then we were just given a practice problem, which was pretty straightforward.

Friday, May 23, 2008

Tuesday, May 20, 2008

Well, another test. This unit hasn't been so bad for me, I understand most of it. Hopefully I do well in the test. I do have a couple of problems with differentiating implicitly but it's nothing practice cannot solve. Otherwise, I'm good to go.

Monday, May 19, 2008

What can I say? Well for one, this unit was simple the second time around =). I really think that I'm going to do well on this next test and yeah, hopefully I don't stumble on something that I haven't yet seen or tried to do. As always, the solution is practice! Hmm, I think the best place to start review would be to go through the past slides, and then see if I have any muddiest points.

This bob was short and straight to the point. I hope everyone remembers to bob and and and! Good luck on the test Wednesday I believe!